As a naive approach, one could try to calibrate ad-hoc weighting coefficients for constraints, in order to find their best linear combination. However, such antagonist dynamics among constraints might occur multiple times during the learning process and also depend on the model initialization. Thus, an approach based on fixed coefficients hardly leads to a solution where the majority of the constraints are satisfied. To this end, we propose to adopt the dual Lagrangian framework [1]} in order to define dynamic coefficients that are periodically updated during learning proportionally to the degree of constraints violation. Under this perspective, a constraint-based problem is relaxed as follows:
\(\mathcal {L} = \operatornamewithlimits{arg\,min}_\theta f_\theta (x) + \lambda g(x)\) 
